Descriptions of reversed yielding of a solid circular bar in torsion

Abstract

Two plastic penetrations are possible from applying torque to a solid, circular-section bar: one from applying an elastic—plastic torque and the other from releasing it. The first penetration occurs from the outer radius inwards towards the centre when the deformation becomes increasingly plastic as the flow stress increases beyond the initial yield stress. The second plastic penetration occurs in a similar manner but is a manifestation of the Bauschinger effect, which refers to that reduction in the flow stress required to initiate reversed plasticity. The latter can occur upon the release of the elastic—plastic torque responsible for an initial plastic penetration, usually deeper than the mean radius. A theory of secondary penetration is given for both linear and parabolic hardening materials. By varying the plastic tangent modulus special cases of linear hardening are studied, including ideal materials with perfect (forward) plasticity and those that obey kinematic hardening. Within the chosen hardening law the elastic and plastic strains are developed from the bar's angular twist within its elastic core. Conditions, for which a torque-release is either purely elastic or elastic—plastic, appear to be within the section parameters and the material's flow curve, these providing the depth of a secondary penetration. Two stress distributions, one for the application of torque and the other for torque release, are sufficient to show that residual stress distributions differ from non-hardening theory. Experimental results given suggest that residuals arising from parabolic hardening are more realistic where a second penetration occurs. Experiment also reveals where kinematic and isotropic hardening models apply.